点此进入淘宝搜索页搜索　　參考價格: 点此进入淘宝搜索页搜索
　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Sergei I. Gelfand，Yuri I. Manin著

出 版 社： 湖南文艺出版社

出版时间： 2003-1-1字数：版次：页数： 372印刷时间： 2003/01/01开本： 16开印次：纸张： 胶版纸I S B N ： 9783540435839包装： 精装内容简介

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

目录

I. Simplicial Sets

1.1 Triangulated Spaces

1.2 Simplicial Sets

1.3 Simplicial Topological Spaces and the Eilenberg-Zilber Theorem

1.4 Homology and Cohomology

1.5 Sheaves

1.6 The Exact Sequence

1.7 Complexes

II. Main Notions of the Category Theory

II.1 The Language of Categories and Functors

II.2 Categories and Structures, Equivalence of Categories

II.3 Structures and Categories. Representable Functors

II.4 Category Approach to the Construction of Geometrical Objects

II.5 Additive and Abelian Categories

II.6 Functors in Abelian Categories

III. Derived Categories and Derived Functors

III.1 Complexes as Generalized Objects

III.2 Derived Categories and Localization

III.3 Triangles as Generalized Exact Triples

III.4 Derived Category as the Localization of Homotopic Category

III.5 The Structure of the Derived Category

III.6 Derived Functors

III.7 Derived Functor of the Composition. Spectral Sequence

III.8 Sheaf Cohomology

IV. Triangulated Categories

IV.1 Triangulated Categories

IV.2 Derived Categories Are Triangulated

IV.3 An Example: The Triangulated Category of A-Modules

IV.4 Cores

V. Introduction to Homotopic Algebra

V.1 Closed Model Categories

V.2 Homotopic Characterization of Weak Equivalences

V.3 DG-Algebras as a Closed Model Category

V.4 Minimal Algebras

V.5 Equivalence of Homotopy Categories

References

Index

 

 

免责声明：本文为网络用户发布，其观点仅代表作者个人观点，与本站无关，本站仅提供信息存储服务。文中陈述内容未经本站证实，其真实性、完整性、及时性本站不作任何保证或承诺，请读者仅作参考，并请自行核实相关内容。